Pivotable computer interface

ABSTRACT

A computer interface for use with a computer simulation system. The interface includes a first grip portion and a second grip portion pivotably coupled to the first grip portion. An actuator is coupled to at least one of the two grip portions and is configured to provide feedback to a user.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/305,958, filed Jul. 16, 2001, entitled“PIVOTABLE COMPUTER INTERFACE,” the contents of which are herebyincorporated in its entirety for all purposes.

BACKGROUND OF THE INVENTION

The present invention relates to interfacing a user with a computer.

Users interface with electronic and mechanical devices in a variety ofapplications, and the need for a more natural, easy-to-use, andinformative interface is a constant concern. In the context of thepresent invention, a user interfaces with computer devices for a varietyof applications. One such application is interacting withcomputer-generated environments, such as virtual reality environments,including surgical simulations, games, actual surgeries and otherapplication program generated environments. Computer input devices suchas mice and trackballs are often used to control a cursor within agraphical environment and provide input in these applications.

In some interface devices, force feedback and/or tactile feedback isalso provided to the user, collectively known herein as “hapticfeedback.” For example, haptic versions of joysticks, mice, gamepads,steering wheels, or other types of devices may output forces to the userbased on events or interactions occurring within the graphicalenvironment, such as in a game or other application program. In acomputer simulation, it is often desirable to graphically represent auser or a portion of the user in the graphical environment and to allowthe user to realistically interact with the graphical environment.

SUMMARY OF THE INVENTION

The present invention provides a computer interface for use with acomputer simulation system. The interface includes a first grip portionand a second grip portion pivotably coupled to the first grip portion.An actuator is coupled to at least one of the two grip portions and isconfigured to provide feedback to a user.

In accordance with one aspect of the present invention, the actuator iscoupled to both the first and second grip portions.

In accordance with another aspect of the present invention, the actuatorcomprises a rotary motor.

In accordance with a further aspect of the present invention, theactuator is coupled to the first grip portion and comprises a rotarymotor, a rotating shaft that extends into the second grip portion and acable coupled to the rotating shaft and the second grip portion.

In accordance with another aspect of the present invention, the computerinterface further includes a spring coupled to both the first and secondgrip portions.

In accordance with a further aspect of the present invention, thecomputer interface includes at least one sensor for sensing angularrotation of a pivot coupling the first and second grip portions.

In accordance with yet a further aspect of the present invention, thefeedback is at least one of a group comprising pushing the grip portionsapart, pulling the grip portions together, vibration, torque and noise.

In accordance with another aspect of the present invention, theinterface comprises a practice tool comprising an elongated portion anda handle. The handle includes the first and second grip portions and theactuator is coupled to at least one of the two grip portions.

In accordance with another aspect of the present invention, a sensor isprovided that senses at least one of motion and position of theelongated portion.

In accordance with another aspect of the present invention, a method ofproviding feedback within a practice tool during computerized simulationincludes providing a practice tool comprising an elongated portion and ahandle, the handle comprises a first grip portion at a proximal portionof the elongated portion, a second grip portion at a proximal portion ofthe elongated portion and pivotably coupled to the first grip portion,and an actuator coupled to at least one of the first and second gripportions. Feedback is provided with the actuator to a user.

Other features and advantages of the present invention will beunderstood upon reading and understanding the description of thepreferred exemplary embodiments, found hereinbelow, in conjunction withreference to the drawings, in which like numerals represent likeelements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a computer interface system accordingto the present invention;

FIG. 2 is a schematic diagram of a computer interface system accordingto the present invention comprising an instrument with a pivotinghandle;

FIG. 3 is a schematic diagram of an embodiment of a haptic interfacedevice according to the present invention;

FIG. 4 is a schematic diagram of another embodiment of a hapticinterface device according to the present invention;

FIG. 5 is a schematic diagram of another embodiment of a hapticinterface device according to the present invention;

FIG. 6 is a schematic diagram of another embodiment of a hapticinterface device according to the present invention;

FIG. 7 is a schematic diagram of another embodiment of a hapticinterface device according to the present invention;

FIG. 8 is a schematic diagram of another embodiment of a hapticinterface device according to the present invention;

FIGS. 9-11 are additional views of the haptic interface device of FIG.8; and

FIG. 12 is a schematic side view of an instrument with a sensor and anactuator.

DESCRIPTION OF EXEMPLARY EMBODIMENTS OF THE INVENTION

The present invention relates to computer simulations and moreparticularly to computer simulations involving the control of agraphical image, such as a graphical image that is a graphicalrepresentation of an instrument being manipulated by a user. Althoughthe process is illustrated at least partly in the context of a surgicalsimulation interface, the present invention may be used in othersimulation and computer interactive processes and/or to control othergraphical images and should not be limited to the examples providedherein.

FIG. 1 is a schematic illustration of a computer interface system 100according to the invention. The computer interface system 100 is capableof generating a computer generated or virtual reality environment. Adisplay 105 provides a graphical environment 110 to a user. Within thegraphical environment 110 is a graphical image 115. The graphical image115 may be, for example, a cursor or other graphical object, theposition, movement, and/or shape of which is controllable. For example,the graphical image 115 may be a pointer cursor, a character in a game,a surgical instrument, a view from the end of a surgical instrument, arepresentative portion of the user, or the like. Also within thegraphical environment is a graphical object 120 such as a round object,as shown, or any other graphical representation including anothergraphical image that may be controlled by the user or by another user. Acontroller 125 in communication with the display 105 is capable ofgenerating and/or controlling the graphical environment 110, for exampleby executing program code including an application program related to asimulation. A user object 130 is manipulatable by a user, and themanipulation of the user object 130 controls the position, orientation,shape and/or other characteristic of the graphical image 115 within thegraphical environment 110, for example by directly correlating aposition of the user object 130 with a displayed position and/or shapeof the graphical image 115 or by correlating a position of the userobject 130 with a rate of movement and/or change of shape of thegraphical image 115. Either the entire user object 130 may bemanipulatable by the user or a portion of the user object 130 may bemanipulatable relative to another portion of the user object 130. Forexample, the user object may be a surface that is engaged by one or morehands of a user, such as a joystick, a mouse, a mouse housing, a stylus,a knob, an elongated rigid or flexible member, an instrumented glove, orthe like and may be moveable in from one to six degrees of freedom.

Optionally, haptic feedback may be provided to the user to increase therealism of the virtual reality environment. For example, when apredetermined event occurs within the graphical environment 110, such asan interaction of the graphical image 115 with the graphical object 120,the controller 125 may cause an actuator 135 to output a hapticsensation to the user. In the version shown, the actuator 135 outputsthe haptic sensation to the user object 130 through which the sensationis provided to the user. The actuator 135 and the user object 130 may bepart of a haptic interface device 140. The actuator 135 may bepositioned in the haptic interface device 140 to apply a force to theuser object 130 or to a portion of the user object.

The actuator 135 may provide the haptic sensation actively or passively.For example, the actuator 135 may comprise one or more motors coupled tothe user object 130 to apply a force to the user or to the user object130 in one or more degrees of freedom. Alternatively or additionally,the actuator 135 may comprise one or more braking mechanisms coupled tothe user object to inhibit movement of the user or the user object 130in one or more degrees of freedom. By haptic sensation it is meant anysensation provided to the user that is related to the user's sense oftouch. For example, the haptic sensation may comprise kinesthetic forcefeedback and/or tactile feedback. By kinesthetic force feedback it ismeant any active or passive force applied to the user to simulate aforce that would be experienced in the graphical environment 110, suchas a grounded force applied to the user or the user object 130 tosimulate a force experienced by at least a portion of the graphicalimage 115. For example, if the graphical image 115 is positioned againsta surface, a barrier or an obstruction, the actuator 135 may output aforce against the user object 130 preventing or retarding movement ofthe user or the user object 130 in the direction of the barrier orobstruction. By tactile feedback it is meant any active or passive forceapplied to the user to provide the user with a tactile indication of apredetermined occurrence within the graphical environment 110. Forexample, a vibration, click, pop, or the like may be output to the userwhen the graphical image 115 interacts with a graphical object 120.Additionally, tactile feedback may comprise a tactile sensation appliedto approximate or give the illusion of a kinesthetic force. For example,by varying the frequency and/or the amplitude of an applied vibration,variations in surface textures of different graphical objects may besimulated or by providing a series of clicks when a graphical imagepenetrates an object, resistance to the penetration may be simulated.For example, in one version a kinesthetic force sensation, such as aspring force, may be applied to the user whenever the graphical image115 engages the graphical object 120 to simulate a selectivelydeformable surface. Alternatively or additionally, a tactile sensation,such as a pop, may be applied to the user when the graphical image 115is moved across a surface of the graphical object 120 to simulate atexture of the graphical object 120.

The controller 125 may be a computer 150, or the like, such as thecomputer shown in FIG. 2. In one version, the computer 150 may comprisea processor and may be able to execute program code. For example, thecomputer may be a personal computer or workstation, such as a PCcompatible computer or Macintosh personal computer, or a Sun or SiliconGraphics workstation. The computer 150 may be operable under theWindows™, MacOS, Unix, or MS-DOS operating system or similar.Alternatively, the computer 150 may be one of a variety of home videogame console systems commonly connected to a television set or otherdisplay, such as systems available from Nintendo, Sega, or Sony. Inother embodiments, the computer 150 may be a “set top box” which may beused, for example, to provide interactive television functions to users,or a “network-” or “internet-computer” which allows users to interactwith a local or global network using standard connections and protocolssuch as used for the Internet and World Wide Web. The computer 150 mayinclude a host microprocessor, random access memory (RAM), read onlymemory (ROM), input/output (I/O) circuitry, and/or other components ofcomputers well-known to those skilled in the art. The computer 150 mayimplement an application program with which a user is interacting viaperipherals, such as haptic interface device 140 and/or user object 130.For example, the application program may be a simulation program, suchas a medical procedure simulation program, a game, a computer aideddesign or other graphic design program, an operating system, a wordprocessor or spreadsheet, a Web page or browser that implements, forexample, HTML or VRML instructions, a scientific analysis program, orother application program that may or may not utilize haptic feedback.Herein, for simplicity, operating systems such as Windows™, MS-DOS,MacOS, Linux, Be, etc. are also referred to as “application programs.”The application program may comprise an interactive graphicalenvironment, such as a graphical user interface (GUI) to allow the userto input information to the program. Typically, the application providesimages to be displayed on a display screen 155 and/or outputs otherfeedback, such as auditory signals. The computer 150 is capable ofgenerating a graphical environment 110, which may be a graphical userinterface, game, simulation, such as those described above, or othervisual environment. The computer 150 displays graphical objects 120,such as graphical representations and graphical images, or “computerobjects,” which are not physical objects, but are logical software unitcollections of data and/or procedures that may be displayed as images bythe computer on display screen 155, as is well known to those skilled inthe art. The application program checks for input signals received fromthe electronics and sensors of the user object 130, and outputs forcevalues and/or commands to be converted into haptic output for theactuator 135. Suitable software drivers which interface such simulationsoftware with computer input/output (I/O) devices are available fromImmersion Corporation of San Jose, Calif. Display screen 155 may beincluded in the computer and may be a standard display screen (LCD, CRT,flat panel, etc.), 3-D goggles, or any other visual output device.

In one version of the computer interface system 100, the user object 130comprises a handle of at least a portion of a real or mock instrument160, such as a surgical instrument used in laparoscopic surgery. In theversion shown in FIG. 2, the instrument 160 comprises a handle having afirst grip 165 and a second grip 170. The first grip 165 and the secondgrip 170 are relatively pivotable about a pivot 175. Manipulation of thehandle may be detected by one or more sensors in, on, or incommunication with the user object 130. A signal indicative of thedetected manipulation is provided to the computer 150, optionallythrough sensor interface 180, to control the position, orientation,and/or shape of the graphical image 115. For example, the sensors maydetect the motion or position of an elongated portion 185 of theinstrument 160 in from one to six or more degrees of freedom to controlthe displayed position of the graphical image 115, as disclosed in U.S.Pat. Nos. 5,623,582; 5,821,920; 5,731,804; and 5,828,197 each of whichis incorporated herein by reference in its entirety. Alternatively oradditionally, one or more sensors may be positioned to detectmanipulation of the first grip 165 relative to the second grip 170, forexample by sensing the amount of rotation about pivot 175. The sensedpivoting may then be used to control the shape of the displayedgraphical image 115. For example, in the version shown, pivoting thefirst grip 165 relative to the second grip 170 may result in an openingor closing of jaws 190 on the distal end of the graphical image 115. Inthis way, a user may be able to manipulate the instrument 160 to causethe graphical image 115 to grasp or otherwise engage the graphicalobject 120.

In use, a user contacts the instrument 160 to interact with thegraphical environment 110. In the version shown in FIG. 2, the usergrasps the handle including the first grip 165 and the second grip 170and manipulates the instrument 160 by causing rotation of the grips andoptionally by manipulating the instrument 160 in additional degrees offreedom. For example, the user may cause the instrument 160 to move tohis or her left and downwardly to cause the graphical image 115 to berendered so as to appear to touch the graphical object 120. In addition,the user may rotate the grips to make the graphical jaws 190 appear tograsp the graphical object 120.

The realism of the graphical environment interaction may be increased byproviding an actuator 135 adapted to provide one or more hapticsensations to the user during the user's interaction with the graphicalenvironment 110. The actuator may either provide the haptic sensationdirectly to the user or may apply the haptic sensation to the userthrough the user object, for example by applying a force to the userthrough the instrument 160. This allows the user to not only visualizethe graphical image 115 contacting the graphical object 120, but also toreceive an indication through the user's sense of touch that the objecthas been contacted, thereby providing a more immersive experience. Inone version, the actuator 135 may be positioned to provide a hapticsensation to the first grip 165 and/or to the second grip 170 tosimulate gripping forces associated with the relative rotation of thegrips. It has been discovered that by providing a haptic sensation tothe user simulating the griping forces, the user's perception ofrealistic interaction with a graphical object 120 is enhanced. Forexample, a haptic sensation may be provided to the grips in coordinationwith the graphical jaws 190 grasping the graphical object 120 tosimulate an actual grasping of an object. Accordingly, in the version ofFIG. 2, the computer 150 controls the output of a haptic sensation tothe instrument 160 by providing a signal, optionally though actuatorinterface 195, to cause the palm forcing mechanism to be actuated.

A version of a haptic interface 140 is shown in FIG. 3. One or moreangle sensors 200 may be positioned to detect the angular rotation aboutthe pivot 175. In a relatively simple version, a single digital oranalog sensor detects either an open condition or a closed condition ofthe grips, and the computer 150 correspondingly displays the graphicaljaws 190 either as being open or as being closed or grasping an objectin the graphical environment 110. In another version, the angle sensor200 may comprise a sensor that provides a variable signal by which thedisplay of the graphical jaws 190 may be controlled. The joint anglesensor may comprise one or more of an optical, electrical, or magneticencoder, a stain gage, a fiber optic sensor, a potentiometer, or thelike. The actuator 135 may be positioned to force apart and/or to bringtogether the first grip 165 and the second grip 170.

An ungrounded version of a haptic interface 140 is shown in FIG. 4. Inthis version, the actuator 135 is housed in or on the second grip 170.The actuator is capable of actuating the first grip 165 toward or awayfrom the second grip 170. With this version, the instrument 160 need notbe grounded in order to provide haptic sensations related to rotation ofthe grips.

The actuator 135 may comprise a rotary motor 135 a, as shown for examplein the version of FIG. 5. In this version, the first grip 165 comprisesan extension 205 and the second grip 170 comprises an extension 215. Theextensions 205, 215 overlap one another as shown in FIG. 5. Theextension 215 of the second grip 170 includes a recessed portion 220which receives the rotary motor actuator 135 a and which grounds themotor 135 a to the second grip 170. The motor 135 a is capable ofrotating a shaft 225 extending therefrom. The shaft 225 extends into arecessed portion 210 in the first grip extension 205. A cable 230 isfixed to the first grip 165, for example, by being fixed to the wall ofthe recessed portion 210 of the extension 205. The other end of thecable 230 is fixed to the rotatable shaft 225, for example by beingfixed within a through bore 235 in the shaft 225. Rotation of the shaft225 in the direction of the arrow causes the cable 230 to wrap aroundthe shaft 225 and pulls the first grip 165 toward the second grip 170.Accordingly, actuation of the motor 135 a may cause a grasping force tobe applied to the instrument 160. This grasping force may be a hapticsensation related to interactions in the graphical environment.Additionally or alternatively, the grasping force may be used toaugment, amplify or reduce the force the user is applying to theinterface device 165. Optionally, a spring 240 which biases the gripstoward an open position may be used to counteract the grasping forcegenerated by the actuator 135 a.

Alternatively, the rotary motor actuator 135 a may be used to generate aforce opposing the closing of the grips, as shown in FIG. 6. In theversion of FIG. 6, the cable 230 is fixed to the opposite side of therecess 210 in the extension 205 of the first grip 165. Thus, as theshaft 225 is rotated in the direction of the arrow in FIG. 6, the firstgrip 165 and the second grip 170 are forced apart. This generated forcemay also be used for haptic sensations. For example, when the graphicaljaws 190 contact the graphical object 120 a force may be output to theuser preventing or inhibiting the closing of the grips in relation tothe displayed activity. Alternatively or additionally, the applied forcemay be used to augment, amplify or reduce the force applied by the user,as discussed above. In the version of the FIG. 6, the spring 240 isoptionally provided to bias the grips towards one another.

Another version of the haptic interface 140 is shown in FIG. 7. In thisversion, the rotary motor actuator 135 a and rotatable shaft 225 areable to actively applied either a closing or an opening force to thegrips. In the version of FIG. 7, the rotatable shaft 225 is used as acapstan-type device. One end of the cable 230 is fixed to one side ofthe recess 210 and the other end of the cable 230 is fixed to the otherside of the recess 210. The cable is wrapped around the rotatable shaft225 and extends through the throughbore 235. Thus, rotation of therotatable shaft 225 in one direction causes an opening force to beapplied to the grips and rotation in the other direction causes aclosing force to be applied to the grips.

FIG. 8 shows a version similar to the version of FIG. 7 but with atapered rotatable shaft 225. The tapered rotatable shaft 225 allows fora greater range of motion between the grips. The taper allows the uptakeof the amount of cable on the shaft to be substantially the same as theamount of cable discharged from the shaft throughout the range of travelof the shaft within the recess 210. In this way, the amount of slack inthe cable is reduced which reduces backlash and which maintains tightcontact of the cable on the shaft. In one version, the tapered shaft 225is conically shaped. In a particularly useful version, the sides of theconically shaped shaft 225 are shaped such that an extension thereofwould result in the sides intersecting substantially at the pivot 175.In another version, the shaft may be stepped.

FIGS. 9 and 10 show top and side perspective views of the hapticinterface device 140 of FIG. 8. FIG. 11 shows the haptic interfacedevice 140 of FIG. 8 with a cover 250 covering the motor 135 a.

FIG. 12 shows a version of in which an actual surgical instrument is theinterface device 140. The surgical instrument, which is a laparoscopicinstrument in the version shown, may include a distal end that iscontrollable by manipulation of the handle. For example, the distal endmay comprise jaws 190 a that may be opened and closed by opening andclosing the grips 165,170 of the handle. The surgical instrument handlemay also comprise an actuator 135, such as one of the actuatingmechanisms discussed above, for forcing the grips open or closed. Theactuator 135 may be used to assist the user in applying forces or may beused to reduce the force a user applies to the grips or may be used toapply a haptic sensation to the user. In one version, a sensor 260 maybe provided to detect a condition at the distal end of the surgicalinstrument. For example, a pressure or force sensor may be positioned todetect the pressure or forces applied to one or more of the jaws 190 ab.The sensed condition may be provided to the controller which may be aseparate controller or may be a controller or logic on the surgicalinstrument. The controller may then control the operation of theactuator 135 in relation to the sensed condition. For example, often themechanical linkage is insufficient to communicate to the user that thejaws have interacted with an object. Thus, the sensor may besufficiently sensitive to detect a predetermined interaction, and thecontroller may cause a haptic response to be applied to the user toindicate the interaction. Additional interactions are discussed in U.S.patent application Ser. No. 09/811,358 filed on Mar. 16, 2001 which isincorporated herein by reference in its entirety.

While this invention has been described in terms of several preferredembodiments, it is contemplated that alterations, permutations andequivalents thereof will become apparent to those skilled in the artupon a reading of the specification and study of the drawings. Forexample, when used with a simulation system, laparoscopic techniquesother than those discussed above may be simulated. For example, othertechniques are disclosed in the following U.S. patents, all of which areincorporated herein by reference in their entireties: U.S. Pat. Nos.5,735,874; 5,514,156; 5,163,945; 5,980,510; 5,632,432; 6,168,605;5,258,004; 5,307,976; 5,447,513; 5,681,324; 6,090,120; and 5,846,254.Additionally, the simulation may comprise surgical applications otherthan laparoscopic procedures. Furthermore, the interface device may beused for non-surgical simulations. For example, an application programmay be responsive to a shear interface and may comprise instructionalprogram code on how to correctly prune a rose bush or a game environmentmay use pivotal grip haptic feedback. Additionally, the forcingmechanisms disclosed may be used to apply forces to relatively pivotingparts in any environment.

1. A computer interface for use with a computer simulation system, thecomputer interface comprising: a first grip portion of the computerinterface; a second grip portion of the computer interface pivotablycoupled to the first grip portion at a pivot point; and an actuatormechanically coupled to the first or second grip portions and configuredto provide haptic feedback to a user, wherein the haptic feedbackcomprises a force about the pivot point applied to one of the first orsecond grip portions.
 2. The computer interface of claim 1, wherein theactuator is coupled to both the first and second grip portions.
 3. Thecomputer interface of claim 2, wherein the actuator comprises a rotarymotor.
 4. The computer interface of claim 1, wherein the actuator iscoupled to the first grip portion and comprises a rotary motor, arotating shaft that extends into the second grip portion, and a cablecoupled to the rotating shaft and the second grip portion.
 5. Thecomputer interface of claim 1, further comprising a spring coupled toboth the first and second grip portions.
 6. The computer interface ofclaim 1, further comprising at least one sensor for sensing angularrotation of the first and second grip portions about the pivot point. 7.The computer interface of claim 1, wherein the haptic feedback comprisesat least one of kinesthetic feedback or vibrotactile feedback.
 8. Acomputer interface for use with a computer simulation system, thecomputer interface comprising a practice tool comprising an elongatedportion and a handle, the handle comprising: a first grip portion of thecomputer interface at a proximal portion of the elongated portion; asecond grip portion of the computer interface at a proximal portion ofthe elongated portion and pivotably coupled to the first grip portion ata pivot point; and an actuator coupled to the first or second gripportions, the actuator configured to provide haptic feedback to a user,wherein the haptic feedback comprises a force about the pivot pointapplied to one of the first or second grip portions.
 9. The computerinterface of claim 8, wherein the actuator is coupled to both the firstand second grip portions.
 10. The computer interface of claim 9, whereinthe actuator comprises a rotary motor.
 11. The computer interface ofclaim 8, wherein the actuator is coupled to the first grip portion andcomprises a rotary motor, a rotating shaft that extends into the secondgrip portion, and a cable coupled to the rotating shaft and the secondgrip portion.
 12. The computer interface of claim 8, further comprisinga spring coupled to both the first and second grip portions.
 13. Thecomputer interface of claim 8, further comprising at least one sensorfor sensing angular rotation of the first and second grip portions aboutthe pivot point.
 14. The computer interface of claim 8, wherein thehaptic feedback comprises at least one of kinesthetic feedback orvibrotactile feedback.
 15. The computer interface of claim 8, furthercomprising at least one sensor for sensing at least one of motion orposition of the elongated portion.
 16. A method of providing hapticfeedback to a practice tool during computerized simulation, the methodcomprising: providing a practice tool comprising an elongated portionand a handle, the handle comprising: a first grip portion of thepractice tool at a proximal portion of the elongated portion; a secondgrip portion of the practice tool at a proximal portion of the elongatedportion and pivotably coupled to the first grip portion at a pivotpoint; and an actuator coupled to the first or second grip portions; andproviding haptic feedback with the actuator, wherein the haptic feedbackcomprises a force about the pivot point applied to one of the first orsecond grip portions.
 17. The method of claim 16, wherein the hapticfeedback comprises at least one of kinesthetic feedback or vibrotactilefeedback.
 18. The method of claim 16, further comprising sensing angularrotation of the first and second grip portions about the pivot point.19. The method of claim 16, further comprising sensing at least one ofmotion or position of the elongated portion.
 20. The method of claim 16,further comprising providing a spring coupled to the first and secondgrip portions.